Problem: As you very well know, this year's funkiest numbers are so called triangular numbers (that is, integers that are representable as <image>, where k is some positive integer), and the coolest numbers are those that are representable as a sum of two triangular numbers.

A well-known hipster Andrew adores everything funky and cool but unfortunately, he isn't good at maths. Given number n, help him define whether this number can be represented by a sum of two triangular numbers (not necessarily different)!

Input

The first input line contains an integer n (1 ≤ n ≤ 109).

Output

Print "YES" (without the quotes), if n can be represented as a sum of two triangular numbers, otherwise print "NO" (without the quotes).

Examples

Input

256


Output

YES


Input

512


Output

NO

Note

In the first sample number <image>.

In the second sample number 512 can not be represented as a sum of two triangular numbers.

Solution (in CPP):

Solution:
#include <bits/stdc++.h>
int main() {
  int n, m;
  int i, j;
  int flag;
  int a[44722];
  for (i = 1; i < 44722; i++) a[i] = i * (i + 1);
  while (scanf("%d", &n) != EOF) {
    n *= 2;
    flag = 0;
    for (i = 1; i < 44721; i++) {
      m = n - a[i];
      for (j = i; j < 44722; j++) {
        if (m == a[j]) {
          flag = 1;
          break;
        }
      }
      if (flag) break;
    }
    if (flag)
      printf("YES\n");
    else
      printf("NO\n");
  }
  return 0;
}